To say that the nation's governors come to the nation's capital at a critical time for their states and their taxpayers would probably be an understatement in the minds of most of them.

But they are coming, today to be exact, and the timing is critical as congressional committees hold hearings all over Capitol Hill on federal budget proposals which would make drastic changes in programs assisting local economies and the lives of the needy.

The National Governors' Association begins its three-day winter meeting today. Headlining its agenda will be the formation of positions on federal budget policy, including the huge federal deficit.

"The governors first passed a deficit position two years ago," Carol Weissert, an NGA spokesperson, recalled. "At that time, some congressmen felt the governors shouldn't be getting involved in matters of congressional concern.

"But now it's important. Many congressmen want the governors' support as they face these decisions. The governors are statewide, elected officials. Their support helps them; it gives them some clout and additional backbone."

Several controversial proposals are expected to be offered as the governors' attempt to "fine-tune" a budget policy during the meeting. Those proposals include recommendations for changes in Social Security, Medicare, and programs with cost-of-living adjustment clauses.

The governors will be asked to go on record in support of a modified flat tax in place of the current federal income tax system, according to Weissert.

And although the governors have enjoyed a positive relationship with Transportation Secretary Elizabeth Dole over the years, transportation budget issues - such as the elimination of Amtrak subsidies and public mass transit operating assistance and the sale of Conrail - may spark dissension when Dole meets with them tomorrow.

Pennsylvania Gov. Dick Thornburgh wears several hats during the winter meeting. He is chairman of the Republican Governors' Association, responsible for laying the groundwork for Republican victories in the gubernatorial elections this year and next. That responsibility can't help but be on his mind as he considers positions on some politically sensitive issues.

Thornburgh is also a member of the Coalition of Northeastern Governors. The northeastern part of the country, according to many of its congressmen, has borne more than its fair share of past federal budget cuts and will suffer again unfairly under the latest Reagan budget proposal.

The Thornburgh administration has yet to take any formal positions on specific budget questions facing the Congress, other than to applaud President Reagan's attempt to reduce thefederal deficit. Thornburgh has not taken a position of the sale of Conrail to the Norfolk Southern Corp. - an issue of major concern to the Northeast and Pennsylvania heavily relied on by the long- term unemployed in Pennsylvania and the Northeast.

During today's meeting of the NGA executive committee, Thornburgh is expected to seek approval, as part of the budget policy, of a resolution calling for a constitutional amendment to require a balanced federal budget.

A balanced budget amendment, he contends, is one of the most effective tools for controlling the federal deficit, and would impose on federal officials the same discipline and prudent management required in 49 of the 50 states.

"It is time that we begin to preach what we practice," Thornburgh said. "This simple but effective requirement would discipline national elected officials to honor their fiscal responsibilities and halt the easy, credit- card type spending which has led to a runaway federal deficit."

Two years ago, a similar proposal offered by a Democratic governor failed to muster enough support to be brought before the entire NGA for a vote, NGA's Weissert recalled. Last year, she said, it was discussed but never voted on by the NGA.

The lack of support for a balanced budget amendment, Weissert explained, should not be viewed as a lack of support for a balanced federal budget.

"Forty-nine states have to balance their budgets, so these governors feel very strongly about it," she said. "They support a balanced federal budget but many feel it shouldn't be made a part of the U.S. Constitution."

Indeed, there is nothing legally preventing President Reagan or Congress from submitting a balanced federal budget. Reagan, who has repeatedly called for a balanced budget amendment to the Constitution, has proposed a 1986 budget that is $180 billion in the red.

Last week during a House Budget Committee hearing, Treasury Secretary James Baker was asked why Reagan did not submit a balanced budget.

"The president asked for a balanced budget amendment . . . but he never thought it should be implemented cold turkey or overnight," Baker said.

A balanced budget, he added, "if presented overnight, would result in some very difficult choices for a lot of people."